In German Patent Publication DE 42 39 579 A1, random wound yarn packages are produced at a winding station of a winding machine having a friction roller for driving the yarn package and sensors for the continuous detection and evaluation of the angular velocities of the friction roller and the yarn package. Specifically, this reference discloses the detection and evaluation of the angular velocities of the friction roller and the yarn package at a winding station for the detection of so-called pattern winding zones and the subsequent initiation of pattern disruption methods when pattern zones are detected in order to prevent or reduce pattern windings on the yarn package. However, the invention of German Patent Publication DE 42 39 579 A1 relates only to pattern windings and there exists a need for a method of monitoring the winding density of the yarn package during the winding operation.